本文關(guān)鍵詞： 稀疏學(xué)習(xí) 矩陣補(bǔ)全 壓縮感知 矩陣分解 隨機(jī)優(yōu)化　出處：《軟件學(xué)報(bào)》2017年06期 　論文類(lèi)型：期刊論文

【摘要】：近年來(lái),隨著壓縮感知技術(shù)在信號(hào)處理領(lǐng)域的巨大成功,由其衍生而來(lái)的矩陣補(bǔ)全技術(shù)也日益成為機(jī)器學(xué)習(xí)領(lǐng)域的研究熱點(diǎn),諸多研究者針對(duì)矩陣補(bǔ)全問(wèn)題展開(kāi)了大量卓有成效的研究.為了更好地把握矩陣補(bǔ)全技術(shù)的發(fā)展規(guī)律,促進(jìn)矩陣補(bǔ)全理論與工程應(yīng)用相結(jié)合,針對(duì)矩陣補(bǔ)全模型及其算法進(jìn)行了綜述.首先,對(duì)矩陣補(bǔ)全技術(shù)進(jìn)行溯源,介紹了從壓縮感知到矩陣補(bǔ)全的自然演化歷程,指出壓縮感知理論的發(fā)展為矩陣補(bǔ)全理論的形成奠定了基礎(chǔ);其次,從非凸非光滑秩函數(shù)松弛的角度將現(xiàn)有矩陣補(bǔ)全模型進(jìn)行分類(lèi),旨在為面向具體應(yīng)用的矩陣補(bǔ)全問(wèn)題建模提供思路;然后綜述了適用于矩陣補(bǔ)全模型求解的代表性?xún)?yōu)化算法,其目的在于從本質(zhì)上理解各種矩陣補(bǔ)全模型優(yōu)化技巧,從而有利于面向應(yīng)用問(wèn)題的矩陣補(bǔ)全新模型求解;最后分析了矩陣補(bǔ)全模型及其算法目前存在的問(wèn)題,提出了可能的解決思路,并對(duì)未來(lái)的研究方向進(jìn)行了展望.
[Abstract]:In recent years, with the great success of compressed sensing technology in the field of signal processing, matrix complement technology derived from it has become a hot topic in the field of machine learning. Many researchers have carried out a great deal of fruitful research on the problem of matrix complement, in order to better grasp the development law of matrix complement technology and promote the combination of matrix complement theory and engineering application, This paper summarizes the matrix complement model and its algorithm. Firstly, the source of matrix complement technology is traced, and the natural evolution from compression perception to matrix complement is introduced. It is pointed out that the development of compressed perception theory lays a foundation for the formation of matrix complement theory. Secondly, the existing matrix complement models are classified from the point of view of nonconvex nonsmooth rank function relaxation. The purpose of this paper is to provide ideas for the modeling of matrix complement problems oriented to specific applications, and then summarize the representative optimization algorithms suitable for solving matrix complement models, the purpose of which is to understand various optimization techniques of matrix complement models in essence. Finally, the problems existing in the matrix complement model and its algorithm are analyzed, the possible solutions are put forward, and the future research direction is prospected.
【作者單位】： 南京航空航天大學(xué)計(jì)算機(jī)科學(xué)與技術(shù)學(xué)院;江蘇省無(wú)線(xiàn)傳感網(wǎng)高技術(shù)研究重點(diǎn)實(shí)驗(yàn)室(南京郵電大學(xué));南京郵電大學(xué)計(jì)算機(jī)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金(61472186,61572263,61403208) 江蘇省自然科學(xué)基金(BK20161516,BK20151511) 中國(guó)博士后科學(xué)基金(2015M581794) 江蘇省高校自然科學(xué)研究面上項(xiàng)目(15KJB520027) 江蘇省博士后科研資助計(jì)劃(1501023C) 南京郵電大學(xué)校級(jí)科研基金(NY214127,NY215097)~~
【分類(lèi)號(hào)】：TP181

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